Problem (REF ) arises in practically every pure and applied discipline, including mathematical programming, engineering, physics, health sciences and economics. As a result, studies of Newton's method form an extremely active area of research, with new variants being constantly developed and tested. Basic results on Newton’s method and comprehensive lists of references can be found, e.g., in the books by Dennis and Schnabel [1]}, Ostrowski [2]}, Ortega and Rheinboldt [3]} and Deuflhard [4]}. The interested reader will find an excellent survey of Newton's method in [5]}.
